The word "ground" used here is the past tense of "grind". Grind is a verb which means to crush something into very small pieces or, to press and rub something on hard surface or between two hard surfaces.
Therefore, you can understand the meaning of this sentence by adding a situation to it, such as - Out of anxiety she rubbed her dirty hands so hard that the dirt on her hands was (in an assuming manner) ground in.
Ground in dirt has penetrated more deeply into the skin than surface dirt. Did you ever dig in the dirt in the yard when you were a kid? You can brush the surface dirt off but your hands are still dirty deep down. This you have to scrub off with soap and water. That is ground in dirt.